A small mass and a thin uniform rod each of mass 'm' are positioned along the same straight line as shown. Find the force of gravitational attraction exerted by the rod on the small mass.

Answer

`(Gm^(2))/(3L^(2))`

Explanation

`dF=(Gm^(2))/(2L)(dx)/(x^(2))`
`F = int_(L)^(3L)(Gm^(2))/(2L)(dx)/(x^(2)) rArr (Gm^(2))/(2L)[-(1)/(x)]_(L)^(3L) rArr (Gm^(2))/(2L)xx[(1)/(L)-(1)/(3L)]`
`F=(Gm^(2))/(2L)xx(2)/(3L) rArr F = (Gm^(2))/(3L^(2))`